1\. An automobile air bag requires about \(62 \mathrm{~L}\) of nitrogen gas in order to inflate. The nitrogen gas is produced by the decomposition of sodium azide, according to the equation shown below $$ 2 \mathrm{NaN}_{3}(s) \rightarrow 2 \mathrm{Na}(s)+3 \mathrm{~N} 2(g) $$ What mass of sodium azide is necessary to produce the required volume of nitrogen at \(25^{\circ} \mathrm{C}\) and 1 atm? 2\. When \(\mathrm{Fe} 2 \mathrm{O}_{3}\) is heated in the presence of carbon, CO 2 gas is produced, according to the equation shown below. A sample of \(96.9\) grams of \(\mathrm{Fe} 2 \mathrm{O}_{3}\) is heated in the presence of excess carbon and the CO2 produced is collected and measured at 1 atm and \(453 \mathrm{~K}\). What volume of \(\mathrm{CO}_{2}\) will be observed? $$ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{~g}) $$ 3\. The reaction of zinc and hydrochloric acid generates hydrogen gas, according to the equation shown below. An unknown quantity of zinc in a sample is observed to produce \(7.50 \mathrm{~L}\) of hydrogen gas at a temperature of \(404 \mathrm{~K}\) and a pressure of \(1.75 \mathrm{~atm} .\) How many moles of zinc were in the sample? $$ \mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl} 2(a q)+\mathrm{H} 2(g) $$

Step by step solution

01

Determine Molar Volume of Gases

At standard temperature and pressure (STP), the molar volume of a gas is 22.4 L/mol. However, since the conditions given are not at STP, use the ideal gas law, PV = nRT, where P is pressure, V is volume, N is number of moles, R is the ideal gas constant, and T is temperature in Kelvin, to find the volume occupied by 1 mole of gas under the given conditions.

02

Calculate Moles of Gas Produced

Use the ideal gas law to calculate the number of moles (n) of nitrogen gas produced in exercise 1 and subsequently for CO2 in exercise 2 using the given temperature and pressure data. The ideal gas constant R is 0.0821 L*atm/(mol*K).

03

Determine Moles of Reactants

Using the stoichiometry of the balanced chemical equations, calculate the number of moles of the reactants (sodium azide for exercise 1, Fe2O3 for exercise 2, and zinc for exercise 3) needed to produce the given moles of gas.

04

Calculate Mass of Reactants

Convert the number of moles of the reactants to mass using their respective molar masses. Sodium azide (NaN3) has a molar mass of 65 g/mol, Fe2O3 has a molar mass of 159.69 g/mol, and Zn has a molar mass of 65.38 g/mol.

05

Solve for the Mass of Sodium Azide

For exercise 1, the number of moles of N2 produced is calculated based on the given volume, temperature, and pressure. Then using the stoichiometry, find the number of moles of NaN3 needed which is then converted to mass.

06

Solve for the Volume of CO2

For exercise 2, first calculate the moles of Fe2O3 based on the given mass and then using stoichiometry find the volume of CO2 produced at the given temperature and pressure.

07

Solve for the Moles of Zinc

For exercise 3, calculate the number of moles of hydrogen gas produced at the given temperature and pressure and then use stoichiometry to determine the moles of zinc that reacted.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products through the breaking and forming of chemical bonds. Understanding these reactions is crucial for solving stoichiometry problems. For instance, chemical reactions describe how sodium azide decomposes to produce nitrogen gas or how iron(III) oxide reacts with carbon to produce carbon dioxide. The key is to balance the equations, which ensures that the law of conservation of mass is adhered to—meaning the number of atoms of each element is the same on both sides of the equation.

Here's a quick rundown on how to tackle chemical reactions in stoichiometry:

• Write down the balanced chemical equation.
• Identify the knowns and unknowns.
• Use mole ratios from the balanced equation to relate the amounts of reactants and products.

Balancing chemical equations is a foundational skill in chemistry that allows us to predict the amounts of substances consumed and produced in a reaction.

Ideal Gas Law

The ideal gas law is a critical equation for chemists that relates the pressure, volume, temperature, and number of moles of a gas. Expressed as PV = nRT, this formula allows us to calculate any one of the variables if the others are known, making it a versatile tool for stoichiometry problems involving gases. In the context of gas collection and measurement, the ideal gas law comes in handy for determining the amount of gas produced in a reaction, like nitrogen in airbags or carbon dioxide when heating iron(III) oxide.

To use the ideal gas law:

• Make sure all units are consistent, with pressure in atm, volume in liters, and temperature in Kelvin.
• Use the ideal gas constant R (0.0821 L*atm/(mol*K)) in calculations.
• Adjust the equation according to the variable you need to solve for.

Understanding this law is vital for predicting how gases will behave under different conditions.

Molar Mass Calculation

Molar mass calculation is another key concept in stoichiometry that refers to the mass of one mole of a substance. It is usually expressed in grams per mole (g/mol) and can be found by summing the atomic masses of the elements present in a compound. For instance, the molar mass of sodium azide (NaN3) and iron(III) oxide (Fe2O3) would be calculated based on the atomic masses of sodium, nitrogen, iron, and oxygen from the periodic table.

Here's how you can approach molar mass calculation:

• Identify the chemical formula of the substance.
• Find the atomic mass of each element in the formula.
• Multiply the atomic mass of each element by the number of atoms of that element in the molecule.
• Add all of the individual masses together to get the total molar mass.

Accurate calculation of molar mass is essential for converting between grams and moles, which is a common procedure in stoichiometry problems.

Gas Collection and Measurement

Gas collection and measurement involves quantifying the gas produced or consumed in a chemical reaction. This process is important in stoichiometry problems where you often need to relate the amount of a gaseous product to the amount of solid or aqueous reactants. The volume of gas is typically measured under particular conditions of temperature and pressure, and can be related to the amount (in moles) using the ideal gas law. For example, in the production of CO2 from the reaction of iron(III) oxide with carbon, the measured volume must be related back to the moles of reactants through stoichiometry.

Common techniques for gas collection include:

• Displacement of water, where the gas is captured over water and the volume is measured.
• Collection in a gas syringe, where the gas’s volume is directly recorded.

It's important to remember that when measuring gas over water, the contribution of water vapor must be accounted for, as the gas collected is actually a mixture of the desired gas and water vapor.